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Question

A small block of mass m is pushed on a smooth track from position A with a velocity 25 times the minimum velocity required to reach point D. When the block reaches point B, what is the direction (in terms of angle with horizontal) of acceleration of the block ?

A
tan1(12)
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B
tan1(2)
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C
sin1(23)
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D
The block never reaches point B
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Solution

The correct option is A tan1(12)
umin=5gR (to just reach D)

Given u=25×5gR
=2gR
At B,
v2B=u22gR(1cos 90)
=4gR2gR
=2gR
For vCM, at=g sin θ and aC=v2R
At B, at=g sin 90=g
ac=2gRR=2g
tan α=atac=g2g=12

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